a) `Z_T =frac{Z_1Z_2}{Z_1 + Z_2}`

`=frac{(200-40j)(60+130j)}{(200-40j)+(60+130j)} `

`=frac{(200-40j)(60+130j)}{260+90j}`

`=frac{(204.0angle-11.31^@)(143.2angle65.22^@)}{(275.1angle19.09^@)}`

`=frac{204.0times143.2}{275.1}angle(-11.31^@+` `65.22^@-` `{:19.09^@)`

`=106.2angle34.82^@`

`=87.18+60.64j`

So we conclude that the total impedance is

`Z_T = 87.2+60.6j\ Omega`


b) We see from the second last line of our last answer that the phase angle is `~~35^@`.


c) Total line current:

We use

So

`I = V/Z`

`=frac{12angle0^@}{106.2angle34.82^@}`

`=0.113angle-34.82^@ "A"`